Journal of Symbolic Logic

Les Automorphismes D'un Ensemble Fortement Minimal

Daniel Lascar

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Let $\mathfrak{M}$ be a countable saturated structure, and assume that $D(\nu)$ is a strongly minimal formula (without parameter) such that $\mathfrak{M}$ is the algebraic closure of $D(\mathfrak{M})$. We will prove the two following theorems: Theorem 1. If $G$ is a subgroup of $\operatorname{Aut}(\mathfrak{M})$ of countable index, there exists a finite set $A$ in $\mathfrak{M}$ such that every $A$-strong automorphism is in $G$. Theorem 2. Assume that $G$ is a normal subgroup of $\operatorname{Aut}(\mathfrak{M})$ containing an element $g$ such that for all $n$ there exists $X \subseteq D(\mathfrak{M})$ such that $\operatorname{Dim}(g(X)/X) > n$. Then every strong automorphism is in $G$.

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J. Symbolic Logic, Volume 57, Issue 1 (1992), 238-251.

First available in Project Euclid: 6 July 2007

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Lascar, Daniel. Les Automorphismes D'un Ensemble Fortement Minimal. J. Symbolic Logic 57 (1992), no. 1, 238--251.

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